Branched extensions of curves in compact surfaces

Author:
Cloyd L. Ezell

Journal:
Trans. Amer. Math. Soc. **259** (1980), 533-546

MSC:
Primary 57M12; Secondary 30C15

DOI:
https://doi.org/10.1090/S0002-9947-1980-0567095-8

MathSciNet review:
567095

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Abstract | References | Similar Articles | Additional Information

Abstract: A *polymersion* is a map where *M* and *N* are compact surfaces, orientable or nonorientable, *M* a surface with boundary, where

(a) At each interior point of *M*, there is an integer such that *F* is topologically equivalent to the complex map in a neighborhood about the point.

(b) At each point *x* in the boundary of *M*, , there is a neighborhood *U* containing *x* such that *U* is homeomorphic to *F*(*U*).

*A normal polymersion* is one where is a normal set of curves in *N*. We are concerned with establishing a combinatorial representation for normal polymersions which map to arbitrary compact surfaces.

**[1]**D. R. J. Chillingworth,*Winding numbers on surfaces*. I, Math. Ann.**196**(1972), 218-249. MR**0300304 (45:9350)****[2]**G. K. Francis,*Assembling compact Riemann surfaces with given boundary curves and branch points on the sphere*, Illinois J. Math.**20**(1976), 198-217. MR**0402776 (53:6590)****[3]**C. L. Ezell and M. L. Marx,*Branched extensions of curves in orientable surfaces*, Trans. Amer. Math. Soc. 259 (1980), 515-532. MR**567094 (81i:57004a)****[4]**M. L. Marx and R. Verhey,*Interior and polynomial extensions of immersed circles*, Proc. Amer. Math. Soc.**24**(1970), 41-49. MR**0252660 (40:5879)****[5]**J. Milnor,*Topology from the differentiable viewpoint*, Univ. Press of Virginia, Charlottesville, Va., 1965.s MR**0226651 (37:2239)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1980-0567095-8

Keywords:
Polymersion,
normal curve,
assemblage,
extension of a normal curve

Article copyright:
© Copyright 1980
American Mathematical Society